The fast Fourier transform (FFT) is a known method of converting a signal into its spectral components for analysis and manipulation. The FFT has utility in a vast variety of applications including signal processing, image enhancement, etc. Unfortunately, the conventional approach to FFTs requires a very large number of complex multiplications and complex additions. These FFT calculations generally require at least a microprocessor with a dedicated math coprocessor to allow execution of the FFT within a period of time suitable for use in real time applications.
In many applications, there is neither the component space, time nor budget allowance available to provide the necessary processing power to compute the FFTs. For example, a conventional FFT performed on a 2048 point input requires on the order of 11,264 complex multiplies and twice that number of complex adds. As is known, complex arithmetic operations require substantially more processing steps as compared to real arithmetic operations. Such demands in processing make real time computations difficult in the absence of high speed, high cost processors and coprocessors. Thus, it has been impractical in the past to utilize FFTs in those applications having space, time or cost constraints.
FFTs are particularly useful in the processing or conditioning of an output signal of a sensor or other type of detection device. For example, different types of sensors (e.g., resistive, capacitive, inductive) are used for sensing parameters such as quantity, pressure, temperature, position, etc. By taking the FFT of the output signal, it is possible to condition the signal in order to obtain information such as phase and amplitude. Unfortunately, it has not always been practical to provide such sensors with the necessary computational hardware. As an example, many aircraft have different sensors which require real time processing. Such sensors frequently require a high speed microprocessor with a dedicated math coprocessor in order to condition the signal using FFTs. This results in increased size and expense making such sensors less attractive in an aircraft environment. In view of the aforementioned shortcomings associated with the conventional use of FFTs, there is a strong need in the art for a signal processing system which utilizes FFTs in such a way that does not require substantial processing power even for real time applications. More specifically, there is a strong need in the art for a system which processes a signal by calculating its FFT without relying upon complex arithmetic operations. Even more specifically, there is a strong need for such a system in a signal conditioner which is capable of processing a signal in real time using simple arithmetic operations.